ROLLBACK make data in INSERTED table is removed in AFTER INSERT TRIGGER

Question

I give an example to show my problem. I created a table like this:

CREATE TABLE a
(
    id INT
)

I then created an AFTER INSERT trigger to not allow insert id = 1 into table a:

CREATE TRIGGER [dbo].[insert_a]
ON [dbo].[a] AFTER INSERT 
AS
BEGIN
    DECLARE @id INT
    SELECT @id = id FROM inserted

    IF @id = 1
    BEGIN
        RAISERROR('1', 12, 1)
        ROLLBACK;
    END

    SELECT * FROM inserted
END

Then I insert id = 1 into table a:

INSERT INTO a VALUES(1)

I get nothing from INSERTED table.

I realize that when I ROLLBACK then + the data in table a was rolled back (I know) and data in INSERTED table is also removed. Why is that?

If I change the AFTER INSERT trigger to an INSTEAD OF INSERT trigger:

ALTER TRIGGER [dbo].[insert_a]
ON [dbo].[a] INSTEAD OF INSERT 
AS
BEGIN
    DECLARE @id INT
    SELECT @id = id FROM inserted

    IF @id = 1
    BEGIN
        RAISERROR('1', 12, 1)
        ROLLBACK
    END

    SELECT * FROM inserted
END

INSERT INTO a VALUES(1)

Then I get the result:

id
1

That means data in INSERTED table is not removed though have been ROLLBACK.

Help me explain deeply what happens inside trigger?

Answer 1

This is the intended behaviour as far as I know. It's just that AFTER may be a bit misleading depending on how you look at it.

"The trigger and the statement that fires it are treated as a single transaction, which can be rolled back from within the trigger. If a severe error is detected, the entire transaction automatically rolls back.".

https://msdn.microsoft.com/en-us/library/ms178110.aspx